Practice Geometric Interpretation - 23.4 | 23. Linear Independence | Mathematics (Civil Engineering -1)
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Geometric Interpretation

23.4 - Geometric Interpretation

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Are the vectors (1,2) and (2,4) linearly independent?

💡 Hint: Check if one can be expressed as a multiple of the other.

Question 2 Easy

Is the set of vectors (3, 1) and (1, -4) linearly independent?

💡 Hint: Consider their direction in the 2D plane.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

Two vectors are linearly independent if they are:

A) Collinear
B) Non-collinear
C) Opposite

💡 Hint: Think about their direction in the plane.

Question 2

In R³, three vectors are linearly independent when they are:

True
False

💡 Hint: Consider the relationship of three planes.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove whether the following set of vectors: (2, 3), (4, 6), and (1, 1) is linearly independent or dependent.

💡 Hint: Use the definition of linear independence to check combinations.

Challenge 2 Hard

Design an example of three vectors in R³ which are linearly independent and explain why.

💡 Hint: Check their arrangement in space.

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Reference links

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